Final answer:
To find the greatest magnitude of acceleration, find the largest absolute value from the given options. Both -3/2 and 3/2 have the largest absolute value, hence indicating the greatest magnitude of acceleration. The direction indicated by the negative sign is not relevant when comparing magnitudes.
Step-by-step explanation:
To determine which answer choice represents the greatest magnitude of acceleration for the block when 1.0-Newton horizontal forces are applied, one should select the answer with the largest absolute value. By considering the absolute value of the given options, we compare 2/3, -3/2, 3/2, and -2/3. The absolute values are 2/3, 3/2, 3/2, and 2/3 respectively. Therefore, choices B) -3/2 and C) 3/2 have the largest absolute values, indicating the greatest magnitude of acceleration. Since they are equal in absolute value, either represents the greatest magnitude. However, because we're focusing on magnitude, the negative sign in option B is irrelevant, thus both B and C have the same magnitude of acceleration.